Properties

Label 9408.bq
Number of curves 2
Conductor 9408
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9408.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bq1 9408bl1 [0, 1, 0, -18440, -765066] [2] 46080 \(\Gamma_0(N)\)-optimal
9408.bq2 9408bl2 [0, 1, 0, 41095, -4634841] [2] 92160  

Rank

sage: E.rank()
 

The elliptic curves in class 9408.bq have rank \(1\).

Modular form 9408.2.a.bq

sage: E.q_eigenform(10)
 
\( q + q^{3} - 4q^{5} + q^{9} + 2q^{11} - 2q^{13} - 4q^{15} - 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.